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A stability theorem for elliptic Harnack inequalities

Richard F. Bass (2013)

Journal of the European Mathematical Society

We prove a stability theorem for the elliptic Harnack inequality: if two weighted graphs are equivalent, then the elliptic Harnack inequality holds for harmonic functions with respect to one of the graphs if and only if it holds for harmonic functions with respect to the other graph. As part of the proof, we give a characterization of the elliptic Harnack inequality.

A strong Liouville theorem for $p$ -harmonic functions on graphs.

Holopainen, Ilkka, Soardi, Paolo M. (1997)

Annales Academiae Scientiarum Fennicae. Mathematica

An asymptotic expansion for the discrete harmonic potential.

Kozma, Gady, Schreiber, Ehud (2004)

Electronic Journal of Probability [electronic only]

An integral related to the Cauchy transform on the Sierpiński gasket.

Dong, Xin-Han, Lau, Ka-Sing (2004)

Experimental Mathematics

Approach regions for trees and the unit disc.

N. Arcozzi, F. Di Biase, R. Urbanke (1996)

Journal für die reine und angewandte Mathematik

Boundary behaviour of eigenfunctions of the Laplace operator on trees

Adam Korányi, Massimo A. Picardello (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Comportement asymptotique des fonctions harmoniques sur les arbres

Frédéric Mouton (2000)

Séminaire de probabilités de Strasbourg

Constructing a Laplacian on the diamond fractal.

Kigami, Jun, Strichartz, Robert S., Walker, Katharine C. (2001)

Experimental Mathematics

Espaces de Dirichlet et capacités fonctionnelles sur des triplets de Hilbert Schmidt

Philippe Paclet (1977/1978)

Séminaire Paul Krée

Existence of feasible potentials on infinite networks.

Oettli, Werner, Yamasaki, Maretsugu (1996)

Journal of Convex Analysis

Exponentials Form a Basis of Discrete Holomorphic Functions on a Compact

Christian Mercat (2004)

Bulletin de la Société Mathématique de France

We show that discrete exponentials form a basis of discrete holomorphic functions on a finite critical map. On a combinatorially convex set, the discrete polynomials form a basis as well.

Fractal Differential Equations on the Sierpinski Gasket.

K. Dalrymple, R.S., Vinson, J.P. Strichartz (1999)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Geometry of compactifications of locally symmetric spaces

Lizhen Ji, Robert Macpherson (2002)

Annales de l’institut Fourier

For a locally symmetric space $M$ , we define a compactification $M \cup M (\infty)$ which we call the “geodesic compactification”. It is constructed by adding limit points in $M (\infty)$ to certain geodesics in $M$ . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give $M (\infty)$ for locally symmetric spaces. Moreover, $M (\infty)$ has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...

On a graph, we give a characterization of a parabolic Harnack inequality and Gaussian estimates for reversible Markov chains by geometric properties (volume regularity and Poincaré inequality).

p-harmonic functions on graphs and manifolds.

Ilkka Holopainen, Paolo M. Soardi (1997)

Manuscripta mathematica

Currently displaying 1 – 20 of 29